This invention relates generally to systems for measuring the size of particles, and, more particularly, relates to apparatus and methods for high resolution measurement of sub-micron and micron particle size distributions using polarization intensity differential scattering.
There are several prior art techniques for measuring the size and distribution of sizes of particles in a sample by using light scattering. Generally, to measure the sizes of individual particles, for example, in a flowing stream of a liquid or gas, the particle-containing sample stream is illuminated by a constant light source and the intensity of light scattered by each particle is detected.
A particle scatters the light by an amount related to the particle size. In general, larger particles scatter more light than do smaller particles. The relationship between the amount of scattering and particle size can be determined either from theoretical calculations or through a calibration process. With a knowledge of this relationship, for a single particle at a time, the detected scattered light intensity provides a direct measure of the particle size.
The distribution of particle sizes in a sample can be determined by individually passing each particle in the sample, or a portion of the sample, through the scattered light detection apparatus, and tabulating the sizes of the various particles. In practice, this method is generally restricted to particles larger than 0.5 microns. Moreover, this method is relatively slow, because particles must be presented and detected individually. This technique is referred to in the prior art as optical particle counting.
Another prior art technique of particle sizing by light scattering is referred to as static or "classical" light scattering. This method is based upon illumination of a sample containing the particles to be sized, followed by the measurement of the intensity of scattered light at several predetermined angles. The intensity of light scattered from a particle is a function of the size of the particle, the wavelength of incident light, and the angle at which the scattered light is collected relative to the incident light. This method of particle sizing based upon the angular dependence of the scattered light intensity can be employed to determine the size distribution of a group of particles.
In particular, for particles larger than approximately one micron, scattering in the near-forward direction is well described by Fraunhofer diffraction theory. The Fraunhofer principle yields the angular distribution of scattered light in the focal plane of a lens. For a given particle having a diameter d, the scattered intensity in the angular direction u is given by
I.sub.d, u =k.sub.1 [(]d.sup.2)/4].sup.2 [2J.sub.1 (k.sub.2 du)/(k.sub.2 du)].sup.2
where
k.sub.1 =a constant; PA1 k.sub.2 =]g; and PA1 cJ(k.sub.2 du)/=a Bessel function PA1 [FL]=focal length of the lens PA1 [theta]=scattering angle in the sample cell.
The Fraunhofer theory, upon which most conventional laser diffraction systems are based, shows that small particles diffract light at high angles while larger particles diffract light at smaller angles. Accordingly, by analyzing the composite diffraction pattern resulting from the scattering of monochromatic light beam by a given sample, and measuring the intensity of light scattered at predetermined angles, it is possible to deduce the size distribution of particles in the sample. This principle is widely used in laser diffraction methods and apparatus.
The following U.S. Pat. Nos. disclose examples of laser diffraction systems for measurement of particle size:
______________________________________ 3,646,652 Bol et al 3,758,787 Sigrist 3,809,478 Talbot 3,873,206 Willcock 4,017,186 Shofner et al 4,037,965 Weiss 4,052,600 Wertheimer 4,099,875 McMahon et al 4,167,335 Williams 4,274,741 Cornillault 4,286,876 Hogg et al 4,341,471 Hogg et al 4,541,719 Wyatt 4,595,291 Tatsuno 4,648,715 Ford, Jr. et al 4,676,641 Bott 4,679,939 Curry ______________________________________
Certain prior art systems, among those disclosed in the above-identified U.S. Pat. Nos., utilize a single-optical-axis system, which may comprise a single lens or an assembly of lenses disposed along the same optical axis, for collecting forward scattered light--in a range of approximately 0.03-30.00 degrees from the axis of the incident beam--and directing the scattered light into 15-50 discrete detector cells, so that each detector cell is illuminated by light scattered from the particles at a particular scattering angle.
Other prior art systems utilize multiple collection lenses, disposed along different optical axes, the lenses being optically connected to a single photodetector via fiber optic or other optical coupling elements.
The configuration of a typical prior art laser diffraction instrument 110 for particle size analysis is illustrated in FIG. 1. The beam from a laser 112 is expanded by a conventional beam expander assembly 114, in order to cover a large number of particles in a sample and to reduce the divergence of the beam. This parallel beam then passes through the sample 116, typically a dispersion contained in a sample holder 118. The sample 116 can be stirred or pumped through the path of the laser beam in a re-circulation system, if the sample is a suspension or emulsion, or blown or sprayed through if the sample is a dry powder or spray. Light 122 scattered in the near-forward angles is collected by a Fourier transform lens configuration 120 and directed toward a multicell detector 124, arranged such that the position of a given particle in the path of the laser beam does not affect the point at which the light diffracted by that particle falls on the detector 124.
Discrete detector segments or cells on the detector 124 sense the intensity of light corresponding to that scattered at different angles to the incident beam. This intensity profile can be provided to a computer 126 where digital processing elements determine the size distribution of the particles passing through the laser beam. The computer 126 can be controlled by input from a keyboard 128, and can provide data output via a display unit 130 and printer 132.
Diffraction-type particle size measurement instruments are widely used for measuring sample materials having a broad size distribution--i.e., a wide size range--such as dust or pigment particles. Because large particles scatter light at small angles to the axis of an incident beam, and smaller particles scatter light at large angles, particle size measuring systems utilizing scattered light detection must be capable of measuring scattered light intensity over a large range of scattering angles. Additionally, because large particles scatter light at small angles, and relatively large changes in their size produce only small changes in scattering angles, it would be advantageous to measure light scattered at small angles with relatively high resolution.
These two requirements pose conflicting demands on a single Fourier transform lens or lens system, such as lens system 20 shown in FIG. 1. The result, in conventional diffraction instruments, is compromised performance at large angles, small angles, or both.
A limited range of measurement angles --approximately 20-60 degrees--can be achieved in a conventional diffraction system for measurement of particle size, using a single Fourier lens and multiple detectors. Alternatively, a wide range of measurement angles, with sparse coverage within the angular measurement range, can be attained with multiple detectors, each coupled with a single lens or system of apertures to define the scattering angle, or by moving a single detector successively to different scattering angles. Each of these approaches has been implemented in certain prior art devices, and each has significant limitations.
In particular, when a single-axis optical system is utilized for collecting scattered light over a wide angular range, a short focal length system can provide detection at large angles, at the cost of compressing low-angle scattered light near the optical axis, where it may be obscured by laser spill-over or rendered unresolvable by the finite size of detector segments.
When attempts are made to overcome these deficiencies by utilizing lenses of longer focal length, further problems arise, especially in measurement of scattered light at higher angles. In particular, the longitudinal displacement of high angle detectors from the optical axis can require large dimensions, resulting in a cumbersome instrument package. The required displacement (R) of detectors from the optical axis is approximately
R=[FL]tan [theta]
where
In addition, such a system would require large diameter lenses for collecting light scattered at large angles, thereby increasing spherical aberration and astigmatism and complicating the positioning of high angle detectors.
Systems which utilize elements for moving a single detector successively to different scattering angles are typically limited by low angular resolution, long measurement times and mechanical complexity.
Accordingly, it is an object of the invention to provide methods and apparatus for analysis of particle size based upon measurement of scattered light, which enable the measurement of scattered light over wide angular ranges.
It is another object of the invention to provide methods and apparatus for measuring particle size with high angular resolution at low scattering angles.
It is a further object of the invention to provide particle size analysis apparatus which is compact and mechanically reliable.
Moreover, although diffraction apparatus can be utilized to measure particles in the 0.1-0.4 micrometers size range, the resolution of conventional methods in this size regime is poor. The loss of resolution is a consequence of the similarity in the angular pattern of scattered light of all particles which are smaller than, or roughly equal in size to, the wavelength of the illuminating light. Since the angular scattering patterns of all particles in this size range are similar, conventional methods are unable to reliably distinguish between particles in this size range.
Another method to measure the sizes of particles in this size range is based on a phenomenon involving the scattering by small particles of light of different polarizations. For particles smaller than the wavelength of the incident light, for scattering at 90 degrees to the direction of the interrogating beam, the light component having a polarization parallel to the scattering plane is scattered much less efficiently that light polarized parallel to the scattering plane. The scattering plane is defined herein as the plane containing the incident light beam and the line connecting the detector to the illuminated part of the sample.
This phenomenon, which is illustrated by the intensity vs. angle plot of FIG. 8, is due to the transverse nature of light. In particular, the electric and magnetic field oscillations which comprise a light beam oscillate in a direction perpendicular to the direction of propagation of the beam.
The difference in the observed intensity of 90 degree scattering light, for a first component of light polarized perpendicular to the scattering plane and a second component of light polarized parallel to the scattering plane, is referred to herein as polarization intensity differential scattering (PIDS). PIDS has been used to measure sizes of particles in the 0.1-0.4 micrometers size range, and can be explained with reference to FIG. 9.
The abscissa on the graph of FIG. 9 represents particle diameter normalized by the wavelength of light. More particularly, the abscissa is a variable conventionally called alpha, given by:
alpha=pi*d/lambda
where d is the Particle diameter, and lambda is the incident light wavelength in the medium surrounding the particles. The ordinate in the graph represents the photodetected PIDS signal per unit mass of particles. The PIDS signal, given by
PIDS=Iperpen,90-Ipara,90
is the unnormalized difference between the scattering intensity at 90 degrees for incident light polarized perpendicular and parallel to the scattering plane.
The wavelength normalized diameter, alpha, is used on the abscissa because all scattering phenomena are dependent on the ratio of particle size to light wavelength, rather than on size alone. Thus the solid line in FIG. 9 can, for example, represent PIDS in the size range of 100 to 1000 nm with light of wavelength 600 nm, or particles in the size range of 200 to 2000 nm with light of wavelength 1200 nm.
The large peak on the left hand side of the graph of FIG. 9 shows that the PIDS signal of particles below alpha=2 is the most significant source of PIDS. This means that that PIDS is sensitive principally to particles smaller than approximately 2/3 the wavelength of the incident light. If a series of PIDS measurements were made, each with light of a different incident light wavelength, a histogram of the particle size distribution could be produced as follows. The shortest wavelength PIDS measurement, for example, at 300 nm, would generally measure the mass of particles below approximately 200 nm. The next measurement might be made at lambda=600 nm. This measurement would be sensitive to particles smaller than approximately 400 nm. By subtracting the first measurement value from the second PIDS measurement value, the mass of particles in the 200-400 nm range could be determined. The third PIDS measurement might be made at 900 nm. By subtracting the second measurement value from the third measurement value, the mass of particles in the size range 400-600 nm would be determined.
This process could be extended indefinitely toward larger or smaller sizes, so long as sources of light of the proper wavelengths are available. In practice, however, conventional diffraction measurements are more suitable for particle sizing above around 1 micrometer and the absorption of UV light by quartz and silica limits the low range endpoint of wavelength to around 150 nm.
This conventional PIDS measurement technique, however, has several significant deficiencies relating to resolution and accuracy. In a measurement such as that described above, it has conventionally been assumed that the PIDS value at any wavelength is sensitive almost exclusively to particles below a certain size. However, the secondary, smaller peaks toward the right hand side of FIG. 9 show that conventional PIDS measurements have substantial response to particles over a range of sizes. Thus a PIDS measurement at, for example, a wavelength of 300 nm will actually be sensitive to a substantial portion of the mass of particles at sizes above 200 nm, with varying sensitivity to the various larger particles, as shown in FIG. 9. This lack of discrimination means that conventional PIDS measurements are subject to serious artifacts and inaccuracies.
A useful "figure-of-merit" (FOM) for evaluating the discrimination of a PIDS measurement is simply the ratio of the area under the curve in the major peak (small alpha value) to the total area under the first peak plus the areas under the subsequent smaller resonance peaks, typically out to five subsequent peaks. This FOM represents the ratio of the sensitivity to the particles of interest to the sensitivity to all particles--including those not of interest. A FOM of 1 would be ideal; a FOM of 0 would mean that the method had no particle sizing discrimination whatsoever. As can be seen from the FIG. 9, the FOM of the conventionally measured PIDS in FIG. 9 is approximately 0.3, indicating a low value of size discrimination.
It is thus a further object of the invention to provide PIDS apparatus and methods having enhanced particle size discrimination.
Other general and specific objects of the invention will in part be obvious and will in part appear hereinafter.